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Journal of the Optical Society of America B

On-axis photon-echo modulation in ruby

Arthur G. Szabo

Published Apr 1, 1986• 15 citations
Publisher

Abstract

Theoretical and experimental studies of photon-echo modulation for the four σ transitions of the R1 line in ruby with an on-axis magnetic field are described. Echoes originating from the Cr3+ ground-state 4A2 (−3/2) spin level (−3/2 echo) are studied for the first time. Unlike ±½ echoes, the −3/2-echo modulation is found to be dominated by Cr–Al interactions occurring outside the 13 inner-shell ions. The +½-echo modulation is observed to be in major disagreement with the theory using previously determined superhyperfine parameters. Regression-analysis studies indicate that this cannot be due solely to parameter errors. Finite nuclear linewidths and/or optical pumping effects are shown to be a plausible source of the disagreement.

DOI
10.1364/josab.3.000514

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Short-Time-Interval Behavior of Photon Echoes in Ruby near Level Crossings

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The behavior of photon echoes near level anticrossings is described in terms of the magnetic-field-dependent mixing parameters. The general features of level-crossing behavior are obscured for most cases in dilute ruby and are dominated instead by strong spin-dependent decay resulting from Cr-Al interactions. However, new experiments at short time separation ($\ensuremath{\tau}=32$ nsec) between pulses have permitted observation of the predicted photon-echo anticrossing signals in ruby, and may be applied to other atomic systems.

Physical Review A•Sep 1, 1973•3 citations
Theoretical and experimental studies of photon-echo modulation for the four σ transitions of the R1 line in ruby with an on-axis magnetic field are described. Echoes originating from the Cr3+ ground-state 4A2 (−3/2) spin level (−3/2 echo) are studied for the first time. Unlike ±½ echoes, the −3/2-echo modulation is found to be dominated by Cr–Al interactions occurring outside the 13 inner-shell ions. The +½-echo modulation is observed to be in major disagreement with the theory using previously determined superhyperfine parameters. Regression-analysis studies indicate that this cannot be due solely to parameter errors. Finite nuclear linewidths and/or optical pumping effects are shown to be a plausible source of the disagreement.
A detailed analysis of the photon-echo decay in dilute ruby is presented. The experimental results are in quantitative agreement with an echo-decay theory based on the magnetic interaction between the Cr electronic spin and neighboring Al nuclear magnetic moments. Specifically, the following photon-echo properties are explained by the Cr-Al interaction: (i) modulation of the echo as a function of pulse separation time, (ii) the rapid decay of the echo from the 4A(ms=32)^{4}A({m}_{s}=\frac{3}{2})4A(ms​=23​) to 2E(ms=12)^{2}E({m}_{s}=\frac{1}{2})2E(ms​=21​) transition, (iii) the dependence of the echo on the direction and magnitude of an external magnetic field, (iv) the echo behavior at the 2.06- and 4.12-kG level crossings, and (v) the photon-echo decay in low magnetic fields. In addition, the experiments presented here show that the Cr-Al magnetic interactions in the 2E^{2}E2E excited state are roughly the same as the corresponding interactions in the 4A2^{4}A_{2}4A2​ ground state. The relationship of the photon-echo results to recent fluorescence-linewidth measurements is discussed.
A stimulated photon echo modulation varying in T (separation between the second and third pulses) due to the superhyperfine interaction between a Cr ion and neighboring Al nuclei has been observed in ruby by using a Stark switching technique. The modulation was observed for a time much longer than T 2 , and much higher resolution was obtained than by two-pulse photon echo experiments. An apparent disagreement between theoretical and experimental modulation patterns was noticed in the region where T > T 2 .
The signals of photon echo (PE) are investigated firstly in a ruby crystal doped only by the 53 Cr isotope ions in a concentration of 0.03 – 0,05 wt%. The optical experiments were performed in backward regime at the wavelength of 693.4 nm both with a low magnetic field (200 G) and without it. Since the 53 Cr isotope ions have hyperfine structure of levels the special attention was paid to the study of the stimulated photon echo and primarily to the investigation of its decay kinetics. It is established that this decay has a form which is typical to the signals of long-lived PE. But in contrast to the long-lived PE the decay time in our case is less than the lifetime of the excited 2E(Ē) state. The signals of primary photon echo and stimulated photon echo at a low longitudinal magnetic field and their decay curves are investigated. We observed the beats of temporal shape of these signals with a period of several tens of nanoseconds. Theoretical analysis shows that they are due to the hyperfine interaction of valence electrons of 53 Cr isotope ions with their own nuclei. The obtained decay curves allow us to estimate the phase relaxation time at the presence of a magnetic field. It proves to be equal to 98 ns. The spectrum of stimulated photon echo signal in the doped ruby exposed to a magnetic field is measured.
A detailed experimental study is reported of the decay of circularly polarized photon echoes as a function of Cr concentration in samples ranging from 0.006 to 1.2 wt.% Cr2{\mathrm{Cr}}_{2}Cr2​O3{\mathrm{O}}_{3}O3​ in Al2{\mathrm{Al}}_{2}Al2​O3{\mathrm{O}}_{3}O3​. The decay is found to be independent of temperature in the liquid-helium range and generally depends on the pulse separation $\ensuremath{\tau}$ as $\mathrm{exp}(\ensuremath{-}K{\ensuremath{\tau}}^{\frac{1}{2}})$ with the decay constant KKK proportional to the square root of the Cr concentration. The measured decay is independent of external magnetic field in the range 1.5-6 kG except at 1.06 kG, where modified decays are observed. A theoretical analysis is made of photon-echo decay in terms of spin flips of echo ions resulting from Cr-Cr magnetic interactions and yields good agreement with the observed decays. Spectral diffusion, modified for photon echoes, is shown not to be an important effect. However, anomalously slow decay is observed in some samples when the laser is tuned to the long-wavelength tail of the sample absorption line and the spectral-diffusion mechanism may apply here. The photon-echo-decay measurements are compared with spin-resonance and available spin-echo data in ruby. Also, it is inferred that resonant optical energy transfer is not an important photon-echo-decay mechanism even in the darkest sample studied.
A photon-echo nuclear double resonance (PENDOR) experiment which detects nuclear magnetic resonances by monitoring the stimulated photon-echo intensity after the application of an rf pulse is described and used to determine the Cr-Al hyperfine and electric-quadrupole interaction parameters associated with the Cr3+{\mathrm{Cr}}^{3+}Cr3+ ion in the 2E(E‾)^{2}E(\overline{E})2E(E) optically excited state in ruby. Most of these parameters are found to be within a few percent of the values associated with Cr3+{\mathrm{Cr}}^{3+}Cr3+ in the 4A2^{4}A_{2}4A2​ ground state. Resonances are also observed associated with the latter, state, and they are in agreement with previous spin-echo ENDOR work. High resolution is obtained by using a gated cw ruby laser which generates a rapid train of three-pulse stimulated-photon echoes with a long time interval between the second and third excitation pulses. The theoretical behavior of the PENDOR effect is discussed with emphasis on the ability to disentangle complicated multiple overlapping resonances by causing whole sets of resonances to disappear in a controlled way.
The behavior of photon echoes near level anticrossings is described in terms of the magnetic-field-dependent mixing parameters. The general features of level-crossing behavior are obscured for most cases in dilute ruby and are dominated instead by strong spin-dependent decay resulting from Cr-Al interactions. However, new experiments at short time separation ($\ensuremath{\tau}=32$ nsec) between pulses have permitted observation of the predicted photon-echo anticrossing signals in ruby, and may be applied to other atomic systems.